Torsional high-pass mechanical filter



Aug. 8, 1950 R. V. L. HARTLEY TORSIONAL HIGH-PASS MECHANICAL FILTER Filed July 1, 1948 INVENTOR y R. MLHARTLEY ATTORNEV Patented Aug. 8, 1950 UNIT-ED STATES PATENT oE-Fics .TOBSIONAL HIGH-PASSMECHANICAL FILTER v Ralph V. L. Hartley, Summit, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application July 1, 1948, Serial No. 36,330

9 -'Claims. 1. 1

This invention relatesto systems for the transmission of mechanical vibrations for such purposes as selecting waves in a given frequency range, or effecting desired delays in transmission.

It is particularly concerned with lowering the cut-off frequency and reducing the amount of space required for a high-pass filter of the type disclosed by E. L. Norton in United States Patent No. 1,799,634, issued April 7, 1931, and entitled Wave Transmission. The Norton invention utilized a piezoelectric crystal to set up torsional vibrations in one end of a rod of uniform circular cross-section bent naturally into helical form. The vibrations were selectively propagated along the rod by virtue of its mechanical characteristics, and applied at the opposite end of the helix to a sec-nd crystal. The stressed crystal produced electrical impulses delayed in time and corresponding to those components of the vibrations applied to the first crystal which were within the selected range of frequencies.

. The mechanical transmission element afforded an extremely sharp discrimination at the lower limit of frequencies permitted to pass, which was highly desirable. Its use for the transmission of audio frequencies of high quality was limited, however, by the size of the apparatus. To obtain a lower cut off at 1000 cycles per second, for example, would have; required a helix substantially four feet in diametenwhile for a 100-cyc1e cutoff the helix required would have a diameter of forty feet.

- I have discovered that this disadvantage may be overcome by forming the helix from a strip of rectangular cross-section with a high ratio of width to thickness, wound with its longer crosssectional dimension extending along a diameter of the helix, and normal to the axis thereof.

This reduces the cut-off frequency so'greatly that the filter may be of a size usable in conventional central ofiiceinstallations on audio frequency circuits. It make possible the convenient use of such equipment in the delay circuit of radar moving target indicator systems. Other examples of the uses to which a solid delay line of convenient size may be applied are found in test equipment for studying fading and other transmission problems on long distance radio circuits, andin equipment for giving a more natural tone to studio broadcasts, where delay circuits are used to simulate echoes.

. e 2 2 e characteristic at substantially reduced frequen cies, orfor a delay line which will pass relatively low frequencies while providing substantial delay.

- periods with a minimum of maintenance.

. The invention may be better understood by reference to the drawings, in which: I

Fig. 1 represents a'unit incorporating the principles of the invention; and Fig. 2 is a fragmentary view partially in section, taken as indicated by line 22 in Fig. 1.

It will be understood that the construction shown is illustrative only of the principles of the invention, and that any equivalent structure may housed within the scope of the appended claims.-

Thefilter assembly is indicated generally a l in Fig. 1 of the drawings. mounting base 2 with upturned 'ends 4 and 5, and may be formed of agood conductor, such as brass. Crystal units Sand 1 are mounted on ends 4 and 5 respectively. Each unit consists of a sodium potassium tartrate or composite Rochelle salt crystal cemented to its supporting end and centrally bored to allow a bolt to pass therethrough. Bolts 9 and 10 act as the internal electrodes, providing electrical connection to thecrystal interior, in which they are fixed in ,accordance with the principles set forth in Nicolson Patents 1,562,578 and 1,574,302.

Bolts 9 and 10 are threaded so that they may be secured to their respective supporting ends 4 and 5. Plates 1 land l2, boredto fit over bolts 9 and l 0, are held against the free ends of the crystals by lock nuts 14 and I5, respectively. If desired, the crystals maybe placed under an initial compression by tightening these nuts. The bolts also provide rigid mechanical support for the crystals relative to their supporting ends 4 and 5. The resilience of the bolts 9 and I0 permits them to transfer torsional movements from the crystal to the helix and vice versa, throughthe coupling 'arrangementsdescribedhereafter The. bolts 9 and lllfare secured at their inner ends to coupling sleeves l6 and l'lby set screwsv 19. The adjacent ends of these sleeves are formed v to receive the ends 20 and 2! of the helix 22; set

screws 24 maintain a rigid connection between the helix ends and the sleeves.

Other applications will occur to those skilled in The helix 22 isshown as having two turns, but the number may be varied as desired to produce therequisite characteristics. I These design principles were set forth inthe Norton patent re-, ferred to above. able metal, suchas steel, brass, copper, aluminum or the like. For each material the proper values.

of the constants ,u, p, and E must, of course, .be

The unit has a heavy It may be of any readily procur- 3 used in computing the performance characteristics.

One electrical connection to each crystal is made by means of conventional girdle electrodes 25 and 25, to which are attached leads 21 and 3t. 5 The other electrical connection, to the interior of each crystal is inad through Ieads-iimand l-E 3!, ends i and 5, and Bolts 9 and NF Anelec trical impulse applied through leads 2'! and 30 will produce a mechanical torsion in the crystal 10 6, which is transmitted through; rod :=9; coupling; 16, helix 22, oupling l1 and rod l'O to crystal I. It there produces mechanical stress in the crystal 1 which results in a potential"afcross leadsfifi a; 3! exactly duplicating that appii'e'd to ileadsrfl and 30, but delayed and attenuated'by the de sired amount.-

Comparing the results of this construction with that of Nortons round rod helix referred to having a cut-ofi atZB'BQO cycles and a helix 2o tefi'r or 13 1" inches a: racemes? witha ratio-i= ziOQtiould 've itslcutofifrequencyredeeea t theimroev .01 2 25 so that: it would-10545925 cycles fier secondiilhste'ad of 3500. Still greater r'eclu tio'ns would;be ob--" tainable-by-reduci-ng--the thickness t'olwidthli'atio'. furthers" Thus-a unit inay be desig ned fiaving a diam-e...

ter 's'ufiiciently small-to "fit 'iylthii'ikany spacetcom ver'iientlyavailable and-yethavinga; desired cute ofij f requencywWhen it to be usedasia delay, line,-additional turns-may baddd a) x the whe'lix' to secureth requisite transmission time through; thesystema U The way -in-which the invention-makes possi ble' a mlIChflOWGl cut-offfrequencyioiith same radius 'of curvature -may cabaretunderstood 7 by onsidering'the-mathe atical-analysis-oftlfe 1 efi'ects-ottorsional vibfatioii of a rod of found 1 cross-section;bent-intda circle; Such'lanalysis I shows- =-that" thecut offi' frqiieney imay- ".b' expressedby the equation "'21s tin where t eensity-ef the -iodi'inaterialia I li -We of rigidity, b the angular displacement in the plane of the cross-section of the rod, and In the moment of inertia of the section about the central axis of the rod normal to the section, it Will be seen that If the rod is now bent into a circle or helix, the cpotential energy factor represented by the left side tEquationiz must be changed, since half th'elrod is put in "compression and half in tension throughout its length when torsion is applied, andathe restoring for'ceis a function of b alone. 1 Letting'Ii represent the moment of inertia of a cross 'sectien ofthe rod about a diameter coinciding withia; diameter of the helix, the potential energy P of the material is which'gives-as restoring forcelEhwhendific feg entiatedewithsrespect to b,

0 b 62b, e-ran m =,r as

Eduati'onIZ then/becomes 6.21) EI 5 25a 5335-31 2 a (5):

" Fdf'the' case'ofn'; rod of circular cross section;

and' -since is 2:2, harmonic ifunctiomrofi q-time Eqli'atibn' fi may be written thxis lifts"; where f is the applied frequency, and theycut n cit-frequency, fc, is'definedase in Equation l.

TheyequatiQlljOf'?mOtiOII .(5),- involved-lathe 1.1 91:

It will beseen from-"Eduatidii l that foii a given't55 In and I1 Fen a rounding};

material '-the cut ofi irquency depends 'onlylon i the radiu s of the coilsriami yai ies inyerse1y3with" that radius 1 The"Norton-patent givesas a prac-I tical'result a cut}ofi "frquency'(if-3500" cycles for J tnl a T Substituting this ratio 'inEq-uatioms -,gi'y,es;-f0 1- a 'steelwire @011 5r, 113i inches iif'diatneteri" T'o' eoikhenpmpagafimaconstant da-anon 1 was deriy'd' frbrifa iconsid'erati'o'rl""IO of "th pr'opa atibneonstant 'fdrithe' filter: which? mvarved equating th"'potntial" and "kinetic 1'6 actions to' obtainthe wavepropaganon equation? Assuming" as 'a starting-Tpoirit that'the "rodfis and thr cut 'oft "frequency becomes, atop the rounds The cut off frequency may then be reduced by; replacing the round rod by one, of cross-section suchthat the ratio Ii/lo iscsmalltcompared with Using. an edg'ewise-wound -helix,'-having the longer dimensio'n of the 'cross,-section,.width- 10;,

stiaigHta-nd "or length Sftliat-p is 'tliecoefiicienvfi normal tothe axis of revolution of the helixpand the "shorter dimension, or thickness t, of the cross- I w To Substituting this equivalent expression in Equation 11, the cut-off frequency fc 'of the edgewise wound strip becomes The ratio of the cut-ofi frequency of the edgewound strip to that of the round rod (Equations 1 and 14) becomes '1 fc p t n E I? 2P That is, the cut-off frequency is reduced by using an edgewise-wound strip in the ratio of the thickness to the width of the tape times the square root of two.

The propagation constant is reduced in the same ratio, so that the distance along the helix at which a given attenuation or phase shift occurs is increased by the reciprocal of this ratio.

It should be observed that the use of tape Wound with the longer cross-sectional dimension parallel to the helix axis would not produce a comparable result. This would make t large compared with w, and Equation 12 would approximate unity, and the ratio of Equation 15 would become, letting ,fcs' represent the cut-off frequency of this helix fig That is, the cut-ofi frequency would then actually be increased over that of the round rod, by the factor It will be seen from the foregoing description that I have made a new and useful contribution to the field of mechanical wave transmission systems, and have thereby increased the field of application of such devices.

What is claimed is:

1. A mechanical wave transmission system, including a helix formed of metal tape having the longer cross-sectional dimension thereof disposed normal to the axis of said helix and the shorter cross-sectional dimension disposed parallel to the axis of said helix, means at one end of said helix for setting up torsional vibration in said tape, and means at the other end of said helix for utilizing torsional vibrations transmitted therethrough.

2. In a mechanical Wave transmission system, a high-pass filter element comprisin a helix formed of a metal tape having its longer crosssectional dimension disposed normal to the axis of said helix and its shorter cross-sectional di mension extending parallel to the axis of said helix, means at one end of said tape for introducing vibration torsionally about the longitudinal axis thereof,- and means, at the opposite end of said tape for utilizing torsional vibrations transmitted therethrough.

3. In a mechanical wave transmission system, a high pass filter having a reduced cut-ofi frequency comprising means for vibrating a member torsionally, a helically formed member adapted to be vibrated in torsion and arranged to have a ratio for a cross-section of said member of substantially less than one-half between I1 and In, where I1 is the moment of inertia of said crosssection about a diameter of said helix passing through said cross-section, and I0 is the moment of inertia of said cross-section about the central axis thereof extending at right angles to said cross-section, and means for receivin torsional vibrationstransmitted through said member.

4.: A high-pass mechanical filter having a low.-

ered cut-off frequency, comprising means for converting electrical impulses into torsional impulses, a solid element arranged to receive said impulses, and means for reconverting said impulses into electrical impulses, wherein said solid element conists of a helix of flat metal tape wound edgewise, and so shaped that a ratio of substantially less than one-half is obtained between I1 and I0 for a cross-section of said tape where I1 is the moment of inertia of said crosssection about a diameter of said helix passing through said cross-section, and I0 is the moment of inertia of said cross-section about th central axis of said cross-section extending normally thereto.

5. In a mechanical wave transmission system, a mechanical high-pass filter comprising a helix formed by a bar having its longer cross-sectional dimension disposed normal to the axis of said helix and its shorter cross-sectional dimension parallel to said axis, wherein the cross-section of said bar has a ratio of substantially less than one-half between the moment of inertia about a line coinciding with a diameter of said helix and the moment of inertia about the central axis of said bar normal to said section, means for applying torsion to one end of said helix, and means for utilizing torsional effects therein at the opposite end of said rod.

6. In a wave transmission system, the combination of a piezoelectric crystal arranged for the production of torsional impulses on the application of electrical potentials thereto; a mechanical element comprising a helix of resilient material joined at one end to said crystal and formed of material having a cross-sectional shape such that the ratio of the moment of inertia of that cross-sectional shape about a diameter of said helix to the moment of inertia of said cross-sectional shape about a central axis normal thereto is substantially less than onehalf; and a second piezoelectric crystal joined to the other end of said helix and arranged to produce electrical impulses on the application thereto of torsional impulses through said helix.

'7. In a mechanical wave transmission system, a delay line comprising a torsion-producing member effective on application thereto of electric potentials, a helix formed of a strip of resilient material connected to said member and having a ratio of substantially less than onehalf between the moment of inertia of the crosssection of said strip about a line therein coinciding with a diameter of said helix and the moment of inertia of said cross-section about the central axis of said strip normal to said section, and a ha ving the longer dimension thereof disposed n the applicatiori" terit lsthemt nbf'fifa] to the axis of sqidhelix and the shorter me eiqq h pd' t lfi he s:

v p it 1 In t 4 otherend ofstid l'iel'ixafid irreziedfo the? duction of electrical impulses correfiohdifi'g tb" 0 to sj gnal impulses tra ggmittgd thereto through I I w REFERENCES CITED lx EEK V i g I; The following references areof fecord in the 511mm ""fig r this patentzf UNITED STATES PATENTS Number Name v Date 20 1;799;63 Nortont; A r.,-7,;:-1-93r 2,455,740 Curtis ::'Dec:"7,:'1948j 

